Configure static files to work with NGINX

Have you tried changing the permissions on your static folder as a test?

Something like:
sudo chmod -R 644 /path/to/static/dir

If that works, also check which posix user is configured in your nginx.conf.

sudo nano /etc/nginx/nginx.conf
# Truncated contents of /etc/nginx/nginx.conf.

...
user ec2-user;  <------- HERE
...
server {
    listen 80;
    server_name example.com;

    location = /favicon.ico { access_log off; log_not_found off; }
    location /static/ {
        root /home/ec2-user/myproject;
    }

    location / {
        include proxy_params;
        proxy_pass http://unix:/home/ec2-user/myproject/myproject.sock;
    }
}
...
sudo nano /etc/nginx/proxy_params
# Contents of /etc/nginx/proxy_params

proxy_set_header Host $http_host;
proxy_set_header X-Real-IP $remote_addr;
proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
proxy_set_header X-Forwarded-Proto $scheme;

Restart NGINX and test.

The above is an example of what I am using currently on my personal blog, using NGINX, Gunicorn and Django.